Day 22 Notebook

Part 1

Playing Jenga with the elves

First, create the bricks

input <- read_lines("Day22Sample.txt")

bricks<-as.data.frame(matrix(ncol=6,nrow=0))
for(i in 1:length(input)){
  bricks<-rbind(bricks,as.numeric(unlist(str_split(str_replace(input[i],"~",","),","))))}
colnames(bricks)<-c("x1","y1","z1","x2","y2","z2")

### add 1 because working with R instead of a language that starts at 0.
bricks<-bricks+1

Now, sort the bricks by the lowest Z, then add a number to show which block is first (& so on)

bricks <- bricks %>% rowwise %>% mutate(lowz=min(z1,z2)) %>% arrange(lowz) %>%
  rowid_to_column(var="bricknum") %>% mutate(bricknum=paste0("brick",bricknum))
bricks[1:5,]

With the bricks sorted, creating an artifical “tower” for them to settle into. It will be a three dimensional array and the lowest layer will be “floor”

Create Container and Graph (mostly for part 2)

tower <- array(character(),
               c(max(bricks$x1,bricks$x2),
                 max(bricks$y1,bricks$y2),
                 max(bricks$z1,bricks$z2)))
tower[,,1]<-"floor"

Function to settle the blocks into the tower and create a support graph:

settle<-function(blist,twr){
  ### create a support graph
  supportgraph<-matrix(ncol=2,nrow=0)
  ### create a new dataframe
  tinyb<-as.data.frame(matrix(ncol=9,nrow=0))
  ### for each row of the bricklist
  for(i in 1:nrow(blist)){
    keepgoing<-TRUE
    currbr<-blist[i,]
    howmanylevels<-dim(twr)[3]
      for(x in currbr$x1:currbr$x2){
        for(y in currbr$y1:currbr$y2){
          for(z in currbr$z1:currbr$z2){
            highestfilled<-max(which(!is.na(twr[x,y,1:(currbr$lowz-1)])))
            howmanylevels<-min(howmanylevels,z-highestfilled-1)}}}
    currbr$z1<-currbr$z1-howmanylevels
    currbr$z2<-currbr$z2-howmanylevels
    currbr$lowz<-currbr$lowz-howmanylevels
    ### once it has dropped as far as possible, add the brickname to the tower
    for(x in currbr$x1:currbr$x2){
      for(y in currbr$y1:currbr$y2){
        for(z in currbr$z1:currbr$z2){
          twr[x,y,z]<-currbr$bricknum
          if(!is.na(twr[x,y,(z-1)])){supportgraph<-rbind(supportgraph,c(twr[x,y,(z-1)],currbr$bricknum))}
          }}}
    ### add the new brick position to the new bricklist
    tinyb<-rbind(tinyb,currbr)}
  ### clean up the repeat edges in the support graph & create the support graph
  supportgraph <- unique(supportgraph)
  supportgraph <-simplify(graph_from_edgelist(as.matrix(supportgraph)))
  colnames(tinyb)<-colnames(blist)
  ### return the updated tower, the new bricklist and the list of all connections between bricks
  list(twr,tinyb,supportgraph)}

Run on the data

settling<-settle(bricks,tower)
settledbricks<-settling[[2]]
settledtower<-settling[[1]]
settledgraph<-settling[[3]]

Here’s a visual of the real data both before and after settling:

The support graph shows a connection between every brick and the bricks it is resting on. A brick is stable if there is a connection between it and the floor.

One way to test is to remove a brick and then see if all of the other bricks still have a connection to the floor. If so, then it can be safely disintegrated. If not, then that brick is not safe

part1<-0
for(i in 1:nrow(settledbricks)){
  checkgraph<-delete.vertices(settledgraph,settledbricks[i,]$bricknum)
  q<-distances(checkgraph,v="floor",to=V(checkgraph),mode=c("out"))[1,]
  if(all(q!=Inf)){part1<-part1+1}}

part1

[1] 5

Part 2 -

Find the chain reactions:

part2<-0

### same as before, but instead of counting the safe bricks, count the number that would fall

for(i in 1:nrow(settledbricks)){
  checkgraph<-delete.vertices(settledgraph,settledbricks[i,]$bricknum)
  q<-distances(checkgraph,v=1,to=V(checkgraph),mode=c("out"))[1,]
  part2<-part2 + length(which(q==Inf))}

part2

[1] 7

day22answers <-function(input){
### set up bricks
  bricks<-as.data.frame(matrix(ncol=6,nrow=0))
for(i in 1:length(input)){
  bricks<-rbind(bricks,as.numeric(unlist(str_split(str_replace(input[i],"~",","),","))))}
colnames(bricks)<-c("x1","y1","z1","x2","y2","z2")

### add 1 because working with R instead of a language that starts at 0.
bricks<-bricks+1
bricks <- bricks %>% rowwise %>% mutate(lowz=min(z1,z2)) %>% arrange(lowz) %>%
  rowid_to_column(var="bricknum") %>% mutate(bricknum=paste0("brick",bricknum))
### set up tower
tower <- array(character(),
               c(max(bricks$x1,bricks$x2),
                 max(bricks$y1,bricks$y2),
                 max(bricks$z1,bricks$z2)))
tower[,,1]<-"floor"

### run settling
settling<-settle(bricks,tower)
settledbricks<-settling[[2]]
settledtower<-settling[[1]]
settledgraph<-settling[[3]]  

### run parts 1 & 2

part1<-0
part2<-0
for(i in 1:nrow(settledbricks)){
  checkgraph<-delete.vertices(settledgraph,settledbricks[i,]$bricknum)
  q<-distances(checkgraph,v="floor",to=V(checkgraph),mode=c("out"))[1,]
  if(all(q!=Inf)){part1<-part1+1}
  part2<-part2 + length(which(q==Inf))}
  c(part1,part2)}

day22 <- day22answers(input)
day22

[1] 5 7